Contract theory

Contract theory

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In economics
Economics
Economics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, contract theory studies how economic actors can and do construct contractual arrangements, generally in the presence of asymmetric information. Because of its connections with both agency
Agency (law)
The law of agency is an area of commercial law dealing with a contractual or quasi-contractual, or non-contractual set of relationships when a person, called the agent, is authorized to act on behalf of another to create a legal relationship with a third party...

 and incentives, contract theory is often categorized within a field known as Law and economics
Law and economics
The economic analysis of law is an analysis of law applying methods of economics. Economic concepts are used to explain the effects of laws, to assess which legal rules are economically efficient, and to predict which legal rules will be promulgated.-Relationship to other disciplines and...

. One prominent application of it is the design of optimal schemes of managerial compensation. In the field of economics, the first formal treatment of this topic was given by Kenneth Arrow
Kenneth Arrow
Kenneth Joseph Arrow is an American economist and joint winner of the Nobel Memorial Prize in Economics with John Hicks in 1972. To date, he is the youngest person to have received this award, at 51....

 in the 1960s.

A standard practice in the microeconomics of contract theory is to represent the behaviour of a decision maker under certain numerical utility structures, and then apply an optimization algorithm to identify optimal decisions. Such a procedure has been used in the contract theory framework to several typical situations, labeled moral hazard
Moral hazard
In economic theory, moral hazard refers to a situation in which a party makes a decision about how much risk to take, while another party bears the costs if things go badly, and the party insulated from risk behaves differently from how it would if it were fully exposed to the risk.Moral hazard...

, adverse selection
Adverse selection
Adverse selection, anti-selection, or negative selection is a term used in economics, insurance, statistics, and risk management. It refers to a market process in which "bad" results occur when buyers and sellers have asymmetric information : the "bad" products or services are more likely to be...

and signalling. The spirit of these models lies in finding theoretical ways to motivate agents to take appropriate actions, even under an insurance contract. The main results achieved through this family of models may involve: mathematical properties of the utility structure of the principal and the agent, relaxation of assumptions, and variations of the time structure of the contract relationship, among others. It is customary to model people as maximizers of some von Neumann-Morgenstern utility functions, as stated by Expected utility theory.

Moral hazard


In moral hazard
Moral hazard
In economic theory, moral hazard refers to a situation in which a party makes a decision about how much risk to take, while another party bears the costs if things go badly, and the party insulated from risk behaves differently from how it would if it were fully exposed to the risk.Moral hazard...

 models, the information asymmetry
Information asymmetry
In economics and contract theory, information asymmetry deals with the study of decisions in transactions where one party has more or better information than the other. This creates an imbalance of power in transactions which can sometimes cause the transactions to go awry, a kind of market failure...

 is the principal's inability to observe and/or verify the agent's action. Performance-based contracts that depend on observable and verifiable output can often be employed to create incentives for the agent to act in the principal's interest. When agents are risk-averse, however, such contracts are generally only second-best
Theory of the Second Best
In welfare economics, the theory of the second best concerns what happens when one or more optimality conditions cannot be satisfied. Canadian economist Richard Lipsey and Australian economist Kelvin Lancaster showed in a 1956 paper that if one optimality condition in an economic model cannot be...

 because incentivization precludes full insurance.

The typical moral hazard model is formulated as follows. The principal solves:

subject to the agent's "individual rationality (IR)" constraint,

and the agent's "incentive compatibility (IC)" constraint,,

where is the wage as a function of output , which in turn is a function of effort. represents the cost of effort, and reservation utility is given by .
is the "utility function", which is concave for the risk-averse agent, is convex for the risk-prone agent, and is linear for the risk-neutral agent.

Adverse selection


In adverse selection
Adverse selection
Adverse selection, anti-selection, or negative selection is a term used in economics, insurance, statistics, and risk management. It refers to a market process in which "bad" results occur when buyers and sellers have asymmetric information : the "bad" products or services are more likely to be...

 models, the principal is not informed about a certain characteristic of the agent. For example, health insurance
Health insurance
Health insurance is insurance against the risk of incurring medical expenses among individuals. By estimating the overall risk of health care expenses among a targeted group, an insurer can develop a routine finance structure, such as a monthly premium or payroll tax, to ensure that money is...

 is more likely to be purchased by people who are more likely to get sick.

Incomplete contracts


Contract theory also utilizes the notion of a complete contract
Complete contract
A complete contract is an important concept from contract theory.If the parties to an agreement could specify their respective rights and duties for every possible future state of the world, their contract would be complete...

, which is thought of as a contract that specifies the legal consequences of every possible state of the world. More recent developments known as the theory of incomplete contracts, pioneered by Oliver Hart and his coauthors, study the incentive effects of parties' inability to write complete contingent contracts, e.g. concerning relationship-specific investments.

Because it would be impossibly complex and costly for the parties to an agreement to make their contract complete, the law provides default rule
Default rule
In legal theory, a default rule is a rule of law that can be overridden by a contract, trust, will, or other legally effective agreement. Contract law, for example, can be divided into two kinds of rules: default rules and mandatory rules. Whereas the default rules can be modified by agreement of...

s which fill in the gaps in the actual agreement of the parties.

During the last 20 years, much effort has gone into the analysis of dynamic contracts. Important early contributors to this literature include, among others, Edward J. Green
Edward J. Green
Edward J. Green is an American economist best known for his contributions to the theory of dynamic contracts. Green received his Ph.D. from Carnegie Mellon University in 1977. His dissertation won him the Alexander Henderson Award for excellence in economics...

, Stephen Spear, and Sanjay Srivastava.

Examples

  • George Akerlof
    George Akerlof
    George Arthur Akerlof is an American economist and Koshland Professor of Economics at the University of California, Berkeley. He won the 2001 Nobel Prize in Economics George Arthur Akerlof (born June 17, 1940) is an American economist and Koshland Professor of Economics at the University of...

     described adverse selection
    Adverse selection
    Adverse selection, anti-selection, or negative selection is a term used in economics, insurance, statistics, and risk management. It refers to a market process in which "bad" results occur when buyers and sellers have asymmetric information : the "bad" products or services are more likely to be...

     in the market for used cars.
  • In certain models, such as Michael Spence
    Michael Spence
    Andrew Michael Spence is an American economist and recipient of the 2001 Nobel Memorial Prize in Economic Sciences, along with George A. Akerlof and Joseph E. Stiglitz, for their work on the dynamics of information flows and market development. He conducted this research while at Harvard University...

    's job-market model, the agent can signal his type to the principal which may help to resolve the problem.

See also

  • Agency cost
    Agency cost
    An agency cost is an economic concept that relates to the cost incurred by an entity associated with problems such as divergent management-shareholder objectives and information asymmetry...

  • Complete contract
    Complete contract
    A complete contract is an important concept from contract theory.If the parties to an agreement could specify their respective rights and duties for every possible future state of the world, their contract would be complete...

  • Contract
    Contract
    A contract is an agreement entered into by two parties or more with the intention of creating a legal obligation, which may have elements in writing. Contracts can be made orally. The remedy for breach of contract can be "damages" or compensation of money. In equity, the remedy can be specific...

  • Contract awarding
    Contract awarding
    Contract awarding is the method used during a procurement in order to evaluate the proposals taking part and award the relevant contract. Usually at this stage the eligibility of the proposals has been concluded...

  • Default rule
    Default rule
    In legal theory, a default rule is a rule of law that can be overridden by a contract, trust, will, or other legally effective agreement. Contract law, for example, can be divided into two kinds of rules: default rules and mandatory rules. Whereas the default rules can be modified by agreement of...

  • New institutional economics
    New institutional economics
    New institutional economics is an economic perspective that attempts to extend economics by focusing on the social and legal norms and rules that underlie economic activity.-Overview:...

  • Mechanism design
    Mechanism design
    Mechanism design is a field in game theory studying solution concepts for a class of private information games...

    : contract theory is an application of mechanism design

External links

  • Bolton, Patrick and Mathias Dewatripont, 2005.: Contract Theory. MIT Press. Description and preview.
  • Dutta, Prajit, and Roy Radner, 1994. "Moral Hazard", in Robert Aumann and Sergiu Hart (eds.). Handbook of game theory. Elsevier. pp. 870–903
  • Laffont, Jean-Jacques
    Jean-Jacques Laffont
    Jean-Jacques Marcel Laffont was a French economist specializing in public economics and information economics. Educated at the University of Toulouse and the Ecole Nationale de la Statistique et de l'Administration Economique in Paris, he was awarded the Ph.D...

    , and David Martimort, 2002. The Theory of Incentives: The Principal-Agent Model. Description, "Introduction," & down for chapter links. (Princeton University Press, 2002)
  • Martimort, David, 2008. "contract theory," The New Palgrave Dictionary of Economics
    The New Palgrave Dictionary of Economics
    The New Palgrave Dictionary of Economics , 2nd Edition, is an eight-volume reference work, edited by Steven N. Durlauf and Lawrence E. Blume. It contains 5.8 million words and spans 7,680 pages with 1,872 articles. Included are 1057 new articles and, from earlier, 80 essays that are designated as...

    , 2nd Edition. Abstract.
  • Salanié, Bernard, 1997. The Economics of Contracts: A Primer. MIT Press, Description (2nd ed., 2005) and chapter-preview links.
  • Tirole, Jean
    Jean Tirole
    Jean Marcel Tirole is a French professor of economics. He works on industrial organization, game theory, banking and finance, and economics and psychology. Tirole is director of the Jean-Jacques Laffont Foundation at the Toulouse School of Economics, and scientific director of the Industrial...

    , 2006. The Theory of Corporate Finance. Princeton University Press. Description.